"It's the most unusual relationship we have with any country in the world," explains US Undersecretary of State for Political Affairs Nicholas Burns.

"It's been 27 years since we've had a normal diplomatic, social and political relationship. And so for instance I am one of the people responsible for Iran in our government and yet I have never met an Iranian government official in my 25-year career."

The fiery rhetoric between Iran and the US of recent months has made it appear that the two countries are on a collision course. But did it have to be this way and could the two sides still sit down face to face?

9/11 opportunity

In the wake of the 11 September 2001 attacks on the US, there were some tentative steps.

In Iran, vast crowds turned out on the streets and held candlelit vigils for the victims. Sixty-thousand spectators respected a minute's silence at Tehran's football stadium.

Iran came close to a war with the Taleban

Some of Iran's leaders also sensed an opportunity. America quickly fixed its sights on the Taleban in Afghanistan with whom the Iranians had nearly come to war just three years earlier.

With a common enemy in the Taleban, the two found grounds to co-operate.

After the Afghan war, US negotiators worked closely with Iranian counterparts to form a new Afghan government.

Some of the talks between US and Iranian officials moved beyond Afghanistan and there was hope that it could lead to tentative re-engagement and eventually a restoration of relations.

But back in their respective capitals, there were voices of dissent.

Debates in Washington and Tehran paralleled each other. Hardliners and moderates clashed about whether it was worth talking to the other side and whether it could ever be trusted.

Hardliners in Iran, scarred by the past, cited Ayatollah Ruhollah Khomeini's dictum that any friendship between the US and Iran was like that between a wolf and a sheep.

And just a few weeks after Iran and the US had worked so closely over Afghanistan, Iran was described by President George W Bush as part of an "axis of evil" in his 2002 State of the Union address.

Javad Zarif, now Iran's ambassador to the United Nations, said this was a big surprise after the co-operation over the Afghan government.

"We were all shocked by the fact that the US had such a short memory and was so ungrateful about what had happened just a month ago," he said.

But the hardliners in Washington had been bolstered by Israel's discovery just a few weeks before the speech of a consignment of arms alleged to be heading from Iran to Palestinian groups.

Surprise overture

Another potential opening came in May 2003.

America's swift march to Baghdad the previous month had led to fears in Tehran that it would be next.

So Tehran made a dramatic - but surprisingly little known - approach to the Americans.

Iran's offer came in the form of a letter, although Iranian diplomats have suggested that their letter was in turn a response to a set of talking points that had come from US intermediaries.

In it, Iran appeared willing to put everything on the table - including being completely open about its nuclear programme, helping to stabilise Iraq, ending its support for Palestinian militant groups and help in disarming Hezbollah.

I believe the nuclear issue could have been resolved long time ago

Javad Zarif, Iran ambassador

What did Iran want? Top of the list was a halt in US hostile behaviour and a statement that "Iran did not belong to 'the axis of evil'".

The letter was the product of an internal debate inside Tehran and had the support of leaders at the highest level.

"That letter went to the Americans to say that we are ready to talk, we are ready to address our issues," explains Seyed Adeli, who was then a deputy foreign minister in Iran. But in Washington, the letter was ignored.

Larry Wilkerson, who was then chief of staff to US Secretary of State Colin Powell, thinks that was a big mistake.

"In my mind it was one of those things you throw up in the air and say I can't believe we did this."

He says the hardliners who stood against dialogue had a memorable refrain. "We don't speak to evil".

The problem was that at the very moment that Iranian vulnerability was at its greatest, thanks to America's swift march to Baghdad, Washington was at its most triumphalist.

Why talk to Iran when you could simply dictate terms from a position of strength?

Gift to the hardliners

The effect of America's rejection of talks was far reaching.

It would tilt the balance of power within Tehran towards the hardliners.

"The failure is not just for the idea, but also for the group who were pursuing the idea," explains Seyed Adeli.

Over the following years, the hardliners in Tehran who were far less supportive of dialogue moved into the ascendancy. And the balance of power between Iran and the US began to shift.

President Ahmadinejad ponders tactics at the UN General Assembly

America's victory in Iraq began to look like something far more ambivalent as a bloody insurgency gathered strength. Meanwhile, Iran's influence both in Iraq and across the Middle East grew, augmented by rising oil prices.

In March 2005, the US announced it would back the EU's negotiations with Iran over its nuclear programme, which Iran says is peaceful but the US and others believe is geared towards weapons.

The possibility of talks is currently on the table. But the US insists that Iran must suspend its nuclear activity first.

At the UN, Iran's ambassador Javad Zarif argues that this is the source of the problem.

"Had it not been for those arbitrary red lines and the pressure that went along with those arbitrary red lines imposed on our negotiating partners, I believe the nuclear issue could have been resolved a long time ago."

But the US believes that Iran has failed to be open about its nuclear programme and needs to abide by UN demands that it halt its activity first.

The two sides may be able to sit down and talk face to face in the coming months, if agreement can be reached regarding some form of Iranian suspension of nuclear activity. But if this chance is lost, there may not be many more.

Mixed Messages and Secret Diplomacy was broadcast on BBC Radio 4 at 8pm on Monday 25 September.